Dividing in a Ratio

A ratio can be used to share out an amount fairly. The trick is to think of the ratio as a recipe of parts, work out what one part is worth, then build each share from it.

Add the parts of the ratio to get the total number of parts.
Divide the amount by the total parts to find the value of one part.
Multiply each number in the ratio by that value to get each share.

For example, share \pounds 20 in the ratio 3 : 2. There are 3 + 2 = 5 parts, so one part is \pounds 20 \div 5 = \pounds 4. The shares are then 3 \times \pounds 4 = \pounds 12 and 2 \times \pounds 4 = \pounds 8 — and notice they add back to \pounds 20.

To share an amount in a given ratio:

the total parts is the sum of the ratio numbers — \text{total} = a + b;
one part is the amount divided by the total parts — \text{one part} = \dfrac{\text{amount}}{a + b};
each share is its ratio number times one part — a \times \text{one part} and b \times \text{one part};
the shares always add back to the original amount.

See it as a bar

Step through how a bar of £20 splits into a 3 : 2 share.